Significant
applications of mathematics to biology have occurred for nearly
a century, starting from the early work of Vito Volterra and
Alfred Lotka on interacting populations, and maturing through
fundamental work in population genetics (Haldane, Fisher, and
Wright), epidemiology (Ross, Kermach and MacKendrick), development
(Turing) and neurobiology (Hodgkin and Huxley, Fitzhugh and
Nagumo, McCulloch and Pitts). Much of this research stimulated
important contributions by other mathematicians (Kolmogorov,
Petrovsky, Piscunox, Karlin, etc.); in general, however, until
the past 10--20 years, communication between mathematicians
and biologists remained problematical; much work in mathematical
biology was relatively sterile, unsullied by contact with data,
while experimental work suffered from a lack of theoretical
generality.

The situation has changed dramatically in the past decade or
so. Today's biologists are, in many areas, very sophisticated
mathematically; mathematicians have learned the importance of
becoming immersed in data; and the spectrum of practitioners
has filled in, providing a continuum of highly mathematical
work to collaborations. New and exciting areas (e.g.
molecular biology, epidemiology and immunology) have opened
up to mathematical investigations. A century of research has
elucidated fundamental mechanisms in evolution, collective phenomena
and pattern formation, and laid the foundations for more specialized
modeling; and the development of new computational tools has
greatly expanded the potential both for fundamental studies
and for communications.

Thus the time is right for this special year at the IMA, built
upon a selected series of workshops highlighting some of the
mathematical challenges emerging from the consideration of biological
issues, and endeavoring to show how the mathematics can be applied
to the resolution of those issues. This program focuses on some
particularly rich areas of investigation, complementing activities
which have been carried out at the IMA in MRI, molecular biology
and neurobiology in earlier years.